Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC for Battery Scheduling Under Forecast Uncertainties
CoRR(2024)
Abstract
Chance constrained stochastic model predictive controllers (CC-SMPC) trade
off full constraint satisfaction for economical plant performance under
uncertainty. Previous CC-SMPC works are over-conservative in constraint
violations leading to worse economic performance. Other past works require
a-priori information about the uncertainty set, limiting their application to
real-world systems. This paper considers a discrete linear time invariant
system with hard constraints on inputs and chance constraints on states, with
unknown uncertainty distribution, statistics, or samples. This work proposes a
novel adaptive online update rule to relax the state constraints based on the
time-average of past constraint violations, for the SMPC to achieve reduced
conservativeness in closed-loop. Under an ideal control policy assumption, it
is proven that the time-average of constraint violations converges to the
maximum allowed violation probability. The time-average of constraint
violations is also proven to asymptotically converge even without the
simplifying assumptions. The proposed method is applied to the optimal battery
energy storage system (BESS) dispatch in a grid connected microgrid with PV
generation and load demand with chance constraints on BESS state-of-charge
(SOC). Realistic simulations show the superior electricity cost saving
potential of the proposed method as compared to the traditional MPC (with hard
constraints on BESS SOC), by satisfying the chance constraints
non-conservatively in closed-loop, thereby effectively trading off increased
cost savings with minimal adverse effects on BESS lifetime.
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